mobius inversion - Sum over divisors of gcd of two numbers

How can I calculate this sum?

$\sum\limits_{d~|~(n_1, n_2)} \mu(d) \tau\left(\dfrac{n_1}{d}\right) \tau\left(\dfrac{n_2}{d}\right)$,

where $(n_1, n_2)$ is gcd of $n_1$ and $n_2$, $\mu$ is Mobius function and $\tau(n)$ is the number of positive divisors of $n$.

I tried to use Mobius inversion formula, but still can't manage to deal with the problem.

Any ideas? Thanks.

P.S. Note that sum in the above equation runs over positive divisors only.